We are aware of the fact that one may perform resummations of the exact results obtained for the Hamiltonian
dynamics to a certain post–Newtonian order, see e.g. [1]}, [2]}, even with a matching
to results from numerical gravity, to be performed in a gauge invariant way. However, it is well–known that
resummations of this kind, also applied in phenomenological implementations of exact quantum field
theoretic
calculations sometimes, cannot accommodate for exact results, since some of the higher order corrections are
necessarily not included. The latter ones may be of the same order or even larger than the resummed terms.
One example can be found in Ref. [3]}.
